Article

Intra Firm Bargaining and Shapley Values

# 15-100/VI (2015-08-18)

Björn Brügemann, VU University Amsterdam; Pieter Gautier, VU University Amsterdam; Guido Menzio, University of Pennsylvania, United States

Keywords:

Intra firm bargaining, Shapley value

JEL codes:

D21, J30

The paper revisits the problem of wage bargaining between a firm and multiple workers. We show that the Subgame Perfect Equilibrium of the extensive-form game proposed by Stole and Zwiebel (1996a) does not imply a profile of wages and profits that coincides with the Shapley values as claimed in their classic paper. We propose an alternative extensive-form bargaining game, the Rolodex Game, that follows a simple and realistic protocol and that, under some mild restrictions, admits a unique Subgame Perfect Equilibrium generating a profile of wages and profits that are equal to the Shapley values. The vast applied literature that refers to the Stole and Zwiebel game to give a game-theoretic foundation to the use of the Shapley values as the outcome of the bargain between a firm and multiple workers should instead refer to the Rolodex game.